Physics:Quantum Lindblad equation - Revision history

WikiHarold: Restore missing Quantum reference definitions

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	* <math>\{\cdot,\cdot\}</math> denotes the anticommutator.		* <math>\{\cdot,\cdot\}</math> denotes the anticommutator.

	The first term gives the usual unitary evolution, while the additional terms describe dissipation, decoherence, and irreversible coupling to the environment.<ref name="MIT_OCW" />		The first term gives the usual unitary evolution, while the additional terms describe dissipation, decoherence, and irreversible coupling to the environment.<ref name="MIT_OCW">{{cite web \|url=https://ocw.mit.edu/courses/22-51-quantum-theory-of-radiation-interactions-fall-2012/resources/mit22_51f12_ch8/ \|title=22.51 Course Notes, Chapter 8: Open Quantum Systems \|website=MIT OpenCourseWare \|access-date=2026-04-12}}</ref>

	=== Hamiltonian part ===		=== Hamiltonian part ===
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	== GKSL structure ==		== GKSL structure ==

	The Lindblad equation is often called the '''GKSL equation''', after Gorini, Kossakowski, Sudarshan, and Lindblad, because the general structure of Markovian quantum master equations was established in parallel by these authors in 1976.<ref name="Lindblad1976" />		The Lindblad equation is often called the '''GKSL equation''', after Gorini, Kossakowski, Sudarshan, and Lindblad, because the general structure of Markovian quantum master equations was established in parallel by these authors in 1976.<ref name="Lindblad1976">{{cite journal \|last=Lindblad \|first=Göran \|title=On the generators of quantum dynamical semigroups \|journal=Communications in Mathematical Physics \|volume=48 \|issue=2 \|pages=119–130 \|year=1976 \|url=https://link.springer.com/article/10.1007/BF01608499 \|doi=10.1007/BF01608499}}</ref>

	Its importance is that it characterizes the generators of completely positive trace-preserving semigroups, which are the physically acceptable Markovian evolutions of open quantum systems.<ref name="Lindblad1976" />		Its importance is that it characterizes the generators of completely positive trace-preserving semigroups, which are the physically acceptable Markovian evolutions of open quantum systems.<ref name="Lindblad1976" />
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	{{#invoke:PhysicsQC\|tocHeadingAndList\|Physics:Quantum basics/See also}}		{{#invoke:PhysicsQC\|tocHeadingAndList\|Physics:Quantum basics/See also}}

	=References=		= References =
	{{reflist\|3}}		{{reflist\|3}}

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	'''Lindblad equation''' ~~is a Book I topic in the Quantum Collection. The Lindblad equation is the standard equation describing the Markovian time evolution of the density operator \rho of an open quantum system. It~~ gives the most general linear dynamical law that preserves trace and complete positivity for a quantum dynamical semigroup. It is fundamental in quantum optics, quantum information, decoherence theory, and the study of dissipative quantum systems~~. The Lindblad equation is the standard equation describing the Markovian time evolution of the density operator \rho of an open quantum system~~. It gives the most general linear dynamical law that preserves trace and complete positivity for a quantum dynamical semigroup. It is fundamental in quantum optics, quantum information, decoherence theory, and the study of dissipative quantum systems.		'''Lindblad equation''' it gives the most general linear dynamical law that preserves trace and complete positivity for a quantum dynamical semigroup. It is fundamental in quantum optics, quantum information, decoherence theory, and the study of dissipative quantum systems. It gives the most general linear dynamical law that preserves trace and complete positivity for a quantum dynamical semigroup. It is fundamental in quantum optics, quantum information, decoherence theory, and the study of dissipative quantum systems. The Lindblad equation is usually written as The first term gives the usual unitary evolution, while the additional terms describe dissipation, decoherence, and irreversible coupling to the environment. is the same as in the von Neumann equation for a closed quantum system.
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	~~The~~ '''Lindblad equation''' is the standard equation describing the Markovian time evolution of the density operator ~~<math>~~\rho~~</math>~~ of an open quantum system. It gives the most general linear dynamical law that preserves trace and complete positivity for a quantum dynamical semigroup.~~<ref name="Lindblad1976">{{cite journal \|last=~~Lindblad ~~\|first=Göran \|title=On~~ the ~~generators~~ of quantum dynamical semigroups \|journal=Communications in Mathematical Physics \|volume=48 \|issue=2 \|pages=119–130 \|year=1976 \|url=https://link.springer.com/article/10.1007/BF01608499 \|doi=10.1007/BF01608499}}</ref><ref name="MIT_OCW">{{cite web \|url=https://ocw.mit.edu/courses/22-51-quantum~~-theory-of-radiation-interactions-fall-2012/resources/mit22_51f12_ch8/ \|title=22~~.~~51 Course Notes, Chapter 8: Open Quantum Systems \|website=MIT OpenCourseWare \|access-date=2026-04-12}}</ref>~~		'''Lindblad equation''' is a Book I topic in the Quantum Collection. The Lindblad equation is the standard equation describing the Markovian time evolution of the density operator \rho of an open quantum system. It gives the most general linear dynamical law that preserves trace and complete positivity for a quantum dynamical semigroup. It is fundamental in quantum optics, quantum information, decoherence theory, and the study of dissipative quantum systems. The Lindblad equation is the standard equation describing the Markovian time evolution of the density operator \rho of an open quantum system. It gives the most general linear dynamical law that preserves trace and complete positivity for a quantum dynamical semigroup. It is fundamental in quantum optics, quantum information, decoherence theory, and the study of dissipative quantum systems.
	It is fundamental in quantum optics, quantum information, decoherence theory, and the study of dissipative quantum systems.~~<ref name="MIT_OCW" />~~
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	== Role in the collection ==		== Role in the collection ==
	This page provides a compact reference point for related pages in Book II. It should be read together with nearby matter-scale topics and the corresponding foundations in [[Physics:Quantum mechanics\|quantum mechanics]].<ref name="matter-wiki">{{cite web \|url=https://en.wikipedia.org/wiki/Quantum_mechanics \|title=Quantum mechanics \|website=Wikipedia \|access-date=2026-05-20}}</ref>		This page provides a compact reference point for related pages in Book II. It should be read together with nearby matter-scale topics and the corresponding foundations in [[Physics:Quantum mechanics\|quantum mechanics]].<ref name="matter-wiki">{{cite web \|url=https://en.wikipedia.org/wiki/Quantum_mechanics \|title=Quantum mechanics \|website=Wikipedia \|access-date=2026-05-20}}</ref>

			== Interpretation ==
			For lindblad equation, the quantum description is useful because it separates the allowed states, interactions, and measurable quantities from the classical picture. The same concept may appear differently in spectroscopy, scattering, condensed matter, field theory, or cosmology.

			== Related measurements ==
			Typical measurements involve spectra, decay products, transition rates, transport behavior, correlation functions, or detector signatures. These observations provide the empirical link between the page topic and the wider Quantum Collection.

	=See also=		=See also=

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	It is therefore one of the central equations of open quantum theory.		It is therefore one of the central equations of open quantum theory.

			== Description ==
			'''Lindblad equation''' is a matter-scale concept used to organize how quantum theory describes atoms, particles, fields, condensed matter, plasma, or spacetime-related systems. In the Quantum Collection it is placed by scale so the reader can move from materials and molecules down to subatomic degrees of freedom.

			== Quantum context ==
			At this scale, the relevant behavior is controlled by quantized states, interactions, conservation laws, and the way excitations or particles are observed. The concept is normally linked to measurable properties such as energy, momentum, charge, spin, spectra, scattering rates, or collective modes.

			== Role in the collection ==
			This page provides a compact reference point for related pages in Book II. It should be read together with nearby matter-scale topics and the corresponding foundations in [[Physics:Quantum mechanics\|quantum mechanics]].<ref name="matter-wiki">{{cite web \|url=https://en.wikipedia.org/wiki/Quantum_mechanics \|title=Quantum mechanics \|website=Wikipedia \|access-date=2026-05-20}}</ref>

	=See also=		=See also=

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	{{Quantum article nav\|previous=Physics:Quantum Master equation\|previous label=Master equation\|next=Physics:Quantum Decoherence\|next label=Decoherence}}		{{Quantum article nav\|previous=Physics:Quantum Master equation\|previous label=Master equation\|next=Physics:Quantum Decoherence\|next label=Decoherence}}